{"paper":{"title":"Quotients, automorphisms and differential operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.GR","authors_text":"Gerald W. Schwarz","submitted_at":"2012-01-30T21:00:47Z","abstract_excerpt":"Let $V$ be a $G$-module where $G$ is a complex reductive group. Let $Z:=\\quot VG$ denote the categorical quotient and let $\\pi\\colon V\\to Z$ be the morphism dual to the inclusion $\\O(V)^G\\subset\\O(V)$. Let $\\phi\\colon Z\\to Z$ be an algebraic automorphism. Then one can ask if there is an algebraic map $\\Phi\\colon V\\to V$ which lifts $\\phi$, i.e., $\\pi(\\Phi(v))=\\phi(\\pi(v))$ for all $v\\in V$. In \\cite{Kuttler} the case is treated where $V=r\\lieg$ is a multiple of the adjoint representation of $G$. It is shown that, for $r$ sufficiently large (often $r\\geq 2$ will do), any $\\phi$ has a lift.\n  We"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.6369","kind":"arxiv","version":9},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}